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Matrix-vector multiplication, the product, c

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Matrix-vector multiplication Matrix-vector multiplication is possible only if the number of columns of the matrix is equal to the length of the vector. A couple of examples of matrixvector multiplication follow: Vector-matrix multiplication, on the other hand, is not defined. This multiplication can be performed, however, as a special case of matrix multiplication as defined next. Matrix multiplication Matrix multiplication is defined by Cm×n = Am×p⋅Bp×n. Notice that matrix multiplication is only possible if the number of columns in the first operand is equal to the number of rows of the second operand. The general term in the product, cij, is defined as p ∑ cij = aik ⋅ bkj , for i = 1,2,K, m; j = 1,2,K, n. k =1 Matrix multiplication is not commutative, i.e., in general, A⋅B ≠ B⋅A. Furthermore, one of the multiplications may not even exist. The following screen shots show the results of multiplications of the matrices that we stored earlier: Page 9-5

Section	Page
Table of Contents	4
Chapter 1	12
Basic Operations	12
Batteries	12
Turning the calculator on and off	13
Adjusting the display contrast	13
Contents of the calculator’s display	14
Menus	14
The TOOL menu	14
Setting time and date	15
Introducing the calculator’s keyboard	15
Selecting calculator modes	17
Operating Mode	18
Number Format and decimal dot or comma	21
Standard format	21
Fixed format with decimals	21
Scientific format	22
Engineering format	23
Decimal comma vs. decimal point	24
Angle Measure	25
Coordinate System	25
Selecting CAS settings	26
Explanation of CAS settings	27
Selecting Display modes	28
Selecting the display font	29
Selecting properties of the line editor	29
Selecting properties of the Stack	30
Selecting properties of the equation writer (EQW)	31
References	31
Chapter 2	32
Calculator objects	32
Editing expressions in the stack	32
Creating arithmetic expressions	32
Creating algebraic expressions	35
Using the Equation Writer (EQW) to create expressions	36
Creating arithmetic expressions	36
Creating algebraic expressions	38
Organizing data in the calculator	39
The HOME directory	39
Subdirectories	40
Variables	40
Typing variable names	40
Creating variables	41
Algebraic mode	41
RPN mode	42
Checking variables contents	44
Algebraic mode	44
RPN mode	44
Using the right-shift key followed by soft menu key labels	44
Listing the contents of all variables in the screen	45
Deleting variables	45
Using function PURGE in the stack in Algebraic mode	45
Using function PURGE in the stack in RPN mode	46
UNDO and CMD functions	47
CHOOSE boxes vs. Soft MENU	47
References	49
Chapter 3	50
Examples of real number calculations	50
Using powers of 10 in entering data	52
Real number functions in the MTH menu	54
Using calculator menus	54
Hyperbolic functions and their inverses	54
Operations with units	56
The UNITS menu	56
Available units	58
Attaching units to numbers	58
Unit prefixes	59
Operations with units	60
Unit conversions	61
Physical constants in the calculator	62
Defining and using functions	64
Reference	65
Chapter 4	66
Definitions	66
Setting the calculator to COMPLEX mode	66
Entering complex numbers	67
Polar representation of a complex number	68
Simple operations with complex numbers	69
The CMPLX menus	69
CMPLX menu through the MTH menu	69
CMPLX menu in keyboard	71
Functions applied to complex numbers	71
Function DROITE: equation of a straight line	72
Reference	72
Chapter 5	74
Entering algebraic objects	74
Simple operations with algebraic objects	75
Functions in the ALG menu	76
Operations with transcendental functions	78
Expansion and factoring using log-exp functions	78
Expansion and factoring using trigonometric functions	79
Functions in the ARITHMETIC menu	80
Polynomials	81
The HORNER function	81
The variable VX	81
The PCOEF function	81
The PROOT function	82
The QUOT and REMAINDER functions	82
The PEVAL function	82
Fractions	82
The SIMP2 function	83
The PROPFRAC function	83
The PARTFRAC function	83
The FCOEF function	83
The FROOTS function	84
Step-by-step operations with polynomials and fractions	84
Reference	85
Chapter 6	86
Symbolic solution of algebraic equations	86
Function ISOL	86
Function SOLVE	87
Function SOLVEVX	89
Function ZEROS	89
Numerical solver menu	90
Polynomial Equations	91
Finding the solutions to a polynomial equation	91
Generating polynomial coefficients given the polynomial's roots	92
Generating an algebraic expression for the polynomial	93
Financial calculations	93
Solving equations with one unknown through NUM.SLV	94
Function STEQ	94
Solution to simultaneous equations with MSLV	95
Reference	96
Chapter 7	98
Creating and storing lists	98
Operations with lists of numbers	98
Changing sign	98
Addition, subtraction, multiplication, division	99
Functions applied to lists	101
Lists of complex numbers	101
Lists of algebraic objects	102
The MTH/LIST menu	102
The SEQ function	104
The MAP function	104
Reference	104
Chapter 8	106
Entering vectors	106
Typing vectors in the stack	106
Storing vectors into variables in the stack	107
Using the Matrix Writer (MTRW) to enter vectors	108
Simple operations with vectors	110
Changing sign	110
Addition, subtraction	110
Multiplication by a scalar, and division by a scalar	111
Absolute value function	111
The MTH/VECTOR menu	111
Magnitude	112
Dot product	112
Cross product	112
Reference	113
Chapter 9	114
Entering matrices in the stack	114
Using the Matrix Writer	114
Typing in the matrix directly into the stack	115
Operations with matrices	116
Addition and subtraction	117
Multiplication	117
Multiplication by a scalar	117
Matrix-vector multiplication	118
Matrix multiplication	118
Term-by-term multiplication	119
Raising a matrix to a real power	119
The identity matrix	120
The inverse matrix	120
Characterizing a matrix (The matrix NORM menu)	121
Function DET	121
Function TRACE	121
Solution of linear systems	122
Using the numerical solver for linear systems	122
Solution with the inverse matrix	124
Solution by “division” of matrices	124
References	125
Chapter 10	126
Graphs options in the calculator	126
Plotting an expression of the form y = f(x)	127
Generating a table of values for a function	129
Fast 3D plots	130
Reference	132
Chapter 11	134
The CALC (Calculus) menu	134
Limits and derivatives	134
Function lim	134
Functions DERIV and DERVX	136
Anti-derivatives and integrals	136
Functions INT, INTVX, RISCH, SIGMA and SIGMAVX	136
Definite integrals	137
Infinite series	138
Functions TAYLR, TAYLR0, and SERIES	138
Reference	139
Chapter 12	140
Partial derivatives	140
Multiple integrals	141
Reference	141
Chapter 13	142
The del operator	142
Gradient	142
Divergence	143
Curl	143
Reference	143
Chapter 14	144
The CALC/DIFF menu	144
Solution to linear and non-linear equations	144
Function LDEC	144
Function DESOLVE	146
The variable ODETYPE	146
Laplace Transforms	147
Laplace transform and inverses in the calculator	147
Fourier series	148
Function FOURIER	148
Fourier series for a quadratic function	149
Reference	150
Chapter 15	152
The MTH/PROBABILITY.. sub-menu - part 1	152
Factorials, combinations, and permutations	152
Random numbers	153
The MTH/PROB menu - part 2	154
The Normal distribution	154
The Student-t distribution	154
The Chi-square distribution	155
The F distribution	155
Reference	155
Chapter 16	156
Entering data	156
Calculating single-variable statistics	157
Sample vs. population	157
Obtaining frequency distributions	158
Fitting data to a function y = f(x)	160
Obtaining additional summary statistics	161
Confidence intervals	162
Hypothesis testing	164
Reference	166
Chapter 17	168
The BASE menu	168
Writing non-decimal numbers	169
Reference	169
Chapter 18	170
Inserting and removing an SD card	170
Formatting an SD card	170
Accessing objects on an SD card	171
Storing objects on the SD card	171
Recalling an object from the SD card	172
Purging an object from the SD card	172
Purging all objects on the SD card (by reformatting)	173
Specifying a directory on an SD card	173
Chapter 19	174
Reference	177
Limited Warranty	178
Service	180
Regulatory information	182